Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES); Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); We consider the Langevin lattice dynamics for a spontaneously broken 44 scalar field theory where both additive and multiplicative noise terms are incorporated. The lattice renormalization for the corresponding stochastic Ginzburg-Landau-Langevin and the subtleties related to the multiplicative noise are investigated. (C) 2012 Elsevier B.V. All rights reserved.

The nonequilibrium dynamics of an homogeneous scalar field is studied using Langevin equations. Microscopic derivations based on quantum field theory methods can lead to complicated nonlocal equations of motion. Here we study, numerically, the results obtained by appropriately approximating these equations in a local form (the Markovian approximation) and compare with results obtained with suitable prescriptions for accounting for the nonlocal terms, i.e. the non-Markovian form. We use a prescription for the nonlocal equations motivated by the results obtained from previous derivations using nonequilibrium quantum field theory methods.

The generalizations of the Langevin equation and the fluctuation-dissipation theorem are discussed in nonequilibrium states. The existence of the general form of the fluctuation-dissipation theorem associated with the Langevin type equation in nonequilibrium states is shown on the basis of a kinematical consideration. The equation of motion for the average fluctuations of dynamical variables in the presence of external fields is discussed within the linear response theory and is reduced to a more useful form by means of the Langevin type equation. The scattering cross section of particles from a system of interacting particles in a nonequilibrium state is also considered in connection with the Langevin type equation.

In this work we investigate the stochastic behavior of a large class of systems with variable damping which are described by a time-dependent Lagrangian. Our stochastic approach is based on the Langevin treatment describing the motion of a classical Brownian particle of mass m. Two situations of physical interest are considered. In the first one, we discuss in detail an application of the standard Langevin treatment (white noise) for the variable damping system. In the second one, a more general viewpoint is adopted by assuming a given expression to the so-called collored noise. For both cases, the basic diffententiaql equations are analytically solved and al the quantities physically relevant are explicitly determined.
The results depend on an arbitrary q parameter measuring how the behavior of the system departs from the standard brownian particle with constant viscosity. Several types of sthocastic behavior (superdiffusive and subdiffusive) are obteinded when the free pamameter varies continuosly.
However, all the results of the conventional Langevin approach with constant damping are recovered in the limit q = 1; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior; Neste trabalho nós investigamos o comportamento estocástico de uma grande classe de sistemas com amortecimento variável descritos por uma lagraniana dependente do tempo. Nossa abordagem estocástica é baseada no formalismo de Langevin descrevendo o comportamento de uma partícula browniana clássica de massa m. Duas situações de interesse físico são consideradas. Inicialmente...

An algorithm for inverse bremsstrahlung heating based on a Langevin equation, suitable for particle-in-cell (PIC) codes, is presented. We consider a quasi-neutral plasma with laser heating as described by inverse bremsstrahlung. This enables the inclusion

We apply complex Langevin dynamics to chiral random matrix theory at nonzero
chemical potential. At large quark mass the simulations agree with the
analytical results while incorrect convergence is found for small quark masses.
The region of quark masses for which the complex Langevin dynamics converges
incorrectly is identified as the region where the fermion determinant
frequently traces out a path surrounding the origin of the complex plane during
the Langevin flow. This links the incorrect convergence to an ambiguity in the
Langevin force due to the presence of the logarithm of the fermion determinant
in the action.; Comment: 23 pages, 10 figures

Langevin forces are investigated in the framework of the phenomenological
Ginzburg-Landau (GL) theory. These stochastic forces introducted in the
time-dependent Ginzburg-Landau (TDGL) equation describing the superconductor
transport properties above the critical temperature model the fluctuations
action. We assume that there exists a profound connection between the
fluctuation Cooper pair energy spectrum and the Langevin forces possible values
spectrum. In investigation carried out on the basis of that hypothesis we
obtain the analytical expression for Langevin forces defining them by means of
order parameter, i.e., by means of the fluctuation Cooper pair wave function.
Langevin forces properties are analyzed. The conlusion about their complex
nature is done. Asymptotic analysis of Langevin forces is performed.; Comment: 8 pages, 0 figures

The stochastic opening and closing of voltage-gated ion channels produces
noise in neurons. The effect of this noise on the neuronal performance has been
modelled using either approximate or Langevin model, based on stochastic
differential equations or an exact model, based on a Markov process model of
channel gating. Yet whether the Langevin model accurately reproduces the
channel noise produced by the Markov model remains unclear. Here we present a
comparison between Langevin and Markov models of channel noise in neurons using
single compartment Hodgkin-Huxley models containing either $Na^{+}$ and
$K^{+}$, or only $K^{+}$ voltage-gated ion channels. The performance of the
Langevin and Markov models was quantified over a range of stimulus statistics,
membrane areas and channel numbers. We find that in comparison to the Markov
model, the Langevin model underestimates the noise contributed by voltage-gated
ion channels, overestimating information rates for both spiking and non-spiking
membranes. Even with increasing numbers of channels the difference between the
two models persists. This suggests that the Langevin model may not be suitable
for accurately simulating channel noise in neurons, even in simulations with
large numbers of ion channels.

Based on the Langevin equation it has been proposed to obtain power curves
for wind turbines from high frequency data of wind speed measurements u(t) and
power output P (t). The two parts of the Langevin approach, power curve and
drift field, give a comprehensive description of the conversion dynamic over
the whole operating range of the wind turbine. The method deals with high
frequent data instead of 10 min means. It is therefore possible to gain a
reliable power curve already from a small amount of data per wind speed.
Furthermore, the method is able to visualize multiple fixed points, which is
e.g. characteristic for the transition from partial to full load or in case the
conversion process deviates from the standard procedures. In order to gain a
deeper knowledge it is essential that the method works not only for measured
data but also for numerical wind turbine models and synthetic wind fields.
Here, we characterize the dynamics of a detailed numerical wind turbine model
and calculate the Langevin power curve for different data samplings. We show,
how to get reliable results from synthetic data and verify the applicability of
the method for field measurements with ultra-sonic, cup and Lidar measurements.
The independence of the fixed points on site specific turbulence effects is
also confirmed with the numerical model. Furthermore...

We introduce two new thermostats, one of Langevin type and one of gradient
(Brownian) type, for rigid body dynamics. We formulate rotation using the
quaternion representation of angular coordinates; both thermostats preserve the
unit length of quaternions. The Langevin thermostat also ensures that the
conjugate angular momenta stay within the tangent space of the quaternion
coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have
constructed three geometric numerical integrators for the Langevin thermostat
and one for the gradient thermostat. The numerical integrators reflect key
properties of the thermostats themselves. Namely, they all preserve the unit
length of quaternions, automatically, without the need of a projection onto the
unit sphere. The Langevin integrators also ensure that the angular momenta
remain within the tangent space of the quaternion coordinates. The Langevin
integrators are quasi-symplectic and of weak order two. The numerical method
for the gradient thermostat is of weak order one. Its construction exploits
ideas of Lie-group type integrators for differential equations on manifolds. We
numerically compare the discretization errors of the Langevin integrators, as
well as the efficiency of the gradient integrator compared to the Langevin ones
when used in the simulation of rigid TIP4P water model with smoothly truncated
electrostatic interactions. We observe that the gradient integrator is
computationally less efficient than the Langevin integrators. We also compare
the relative accuracy of the Langevin integrators in evaluating various static
quantities and give recommendations as to the choice of an appropriate
integrator.; Comment: 16 pages...

In this paper, we consider Langevin processes with mechanical constraints.
The latter are a fundamental tool in molecular dynamics simulation for sampling
purposes and for the computation of free energy differences. The results of
this paper can be divided into three parts. (i) We propose a simple
discretization of the constrained Langevin process based on a standard
splitting strategy. We show how to correct the scheme so that it samples {\em
exactly} the canonical measure restricted on a submanifold, using a Metropolis
rule in the spirit of the Generalized Hybrid Monte Carlo (GHMC) algorithm.
Moreover, we obtain, in some limiting regime, a consistent discretization of
the overdamped Langevin (Brownian) dynamics on a submanifold, also sampling
exactly the correct canonical measure with constraints. The corresponding
numerical methods can be used to sample (without any bias) a probability
measure supported by a submanifold. (ii) For free energy computation using
thermodynamic integration, we rigorously prove that the longtime average of the
Lagrange multipliers of the constrained Langevin dynamics yields the gradient
of a rigid version of the free energy associated with the constraints. A second
order time discretization using the Lagrange multipliers is proposed. (iii) The
Jarzynski-Crooks fluctuation relation is proved for Langevin processes with
mechanical constraints evolving in time. An original numerical discretization
without time-step error is proposed. Numerical illustrations are provided for
(ii) and (iii).

In this article we develop geometric versions of the classical Langevin
equation on regular submanifolds in euclidean space in an easy, natural way and
combine them with a bunch of applications. The equations are formulated as
Stratonovich stochastic differential equations on manifolds. The first version
of the geometric Langevin equation has already been detected before by
Leli\`evre, Rousset and Stoltz with a different derivation. We propose an
additional extension of the models, the geometric Langevin equations with
velocity of constant absolute value. The latters are seemingly new and provide
a galaxy of new, beautiful and powerful mathematical models. Up to the authors
best knowledge there are not many mathematical papers available dealing with
geometric Langevin processes. We connect the first version of the geometric
Langevin equation via proving that its generator coincides with the generalized
Langevin operator proposed by Soloveitchik, Jorgensen and Kolokoltsov. All our
studies are strongly motivated by industrial applications in modeling the fiber
lay-down dynamics in the production process of nonwovens. We light up the
geometry occuring in these models and show up the connection with the spherical
velocity version of the geometric Langevin process. Moreover...

In this paper we formulate a risk-sensitive optimal control problem for continuously monitored open quantum systems modelled by quantum Langevin equations. The optimal controller is expressed in terms of a modified conditional state, which we call a risk-sensitive state, that represents measurement knowledge tempered by the control purpose. One of the two components of the optimal controller is dynamic, a filter that computes the risk-sensitive state. The second component is an optimal control feedback function that is found by solving the dynamic programming equation. The optimal controller can be implemented using classical electronics. The ideas are illustrated using an example of feedback control of a two-level atom.

We derive a generalized Langevin Equation (GLE) for the evolution of an arbitrary phase variable in a classical fluid that is initially at equilibrium and is subsequently subjected to an external field and a thermostat of the type used in nonequilibrium molecular dynamics computer simulations. The nonequilibrium steady state GLE is shown to have the same form as the equilibrium GLE at long times. We use our generalized Langevin equation to derive a simple Langevin equation for the motion of a single heavy Brownian particle in a solvent under steady state planar shear.

Using the Langevin dynamics technique, we have carried out simulations of a single-chain flexible diblock copolymer. The polymer consists of two blocks of equal length, one very poorly solvated and the other close to θ-conditions. We study what happens w